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中文摘要：
针对经典的总变分（TV）去噪模型容易导致阶梯效应的缺陷，提出了一种自适应的二阶总广义变分（TGV）图像恢复模型。通过在二阶TGV正则项中引入边缘指示函数，并利用边缘指示函数在平滑区域，增强扩散，去除噪声，在边缘处降低扩散，保护边缘等特征恢复图像，在新模型中，自适应二阶总广义变分是正则项，它能自动的平衡一阶和二阶导数项。因此这些特征使得新模型在去噪的同时不但能够自适应地保持图像的边缘信息，而且还能去除阶梯效应。为了有效的计算该模型，本文采用原始一对偶算法仿真新模型，实验结果表明，与经典的TV模型相比，改进的方法无论是在视觉效果还是信噪比（SNR）上都有明显地提高。
英文摘要：
Aimming at the drawback of the classical total vaiational denoising model in which the staircas- ing effect is often produced, an improved image restoration model based on adaptive second order total generalized variation （TGV） is proposed in this paper. In the new model, an edge indicator function is in- troduced in the regularization term of second order total generalized variation. The proposed model makes use of the advantages of the edge indicator function that can improve the diffusion and remove the noise in the image smooth region,and reduce the diffusion and protect the edges in the image non-smooth re- gion to restore the noisy image. The adaptive second order total gneralized vairation is the regularization term in the proposed model ,which can automatically balance the first order and second order derivative. So these characteristics make the new model preserve the edge information better and avoid the staircas- ing effect while removing noise. In order to solve the proposed model effectively,the primal-dual method is used in this paper. The experimental results show that compared with the existing congeneric algo- rithms, the new model removes the existing noise effectively and preserves the edges of image while avoi- cling the staircasing effect. Therefore, the restored results are improved in both visual effects and signal to noise ratio （SNR）.
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